Image collection pop-up: 3D reconstruction and clustering of rigid and non-rigid categories

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper introduces an approach to simultaneously estimate 3D shape, camera pose, and object and type of deformation clustering, from partial 2D annotations in a multi-instance collection of images. Furthermore, we can indistinctly process rigid and non-rigid categories. This advances existing work, which only addresses the problem for one single object or, if multiple objects are considered, they are assumed to be clustered a priori. To handle this broader version of the problem, we model object deformation using a formulation based on multiple unions of subspaces, able to span from small rigid motion to complex deformations. The parameters of this model are learned via Augmented Lagrange Multipliers, in a completely unsupervised manner that does not require any training data at all. Extensive validation is provided in a wide variety of synthetic and real scenarios, including rigid and non-rigid categories with small and large deformations. In all cases our approach outperforms state-of-the-art in terms of 3D reconstruction accuracy, while also providing clustering results that allow segmenting the images into object instances and their associated type of deformation (or action the object is performing).Postprint (author's final draft

Multi-body Non-rigid Structure-from-Motion

Conventional structure-from-motion (SFM) research is primarily concerned with the 3D reconstruction of a single, rigidly moving object seen by a static camera, or a static and rigid scene observed by a moving camera --in both cases there are only one relative rigid motion involved. Recent progress have extended SFM to the areas of {multi-body SFM} (where there are {multiple rigid} relative motions in the scene), as well as {non-rigid SFM} (where there is a single non-rigid, deformable object or scene). Along this line of thinking, there is apparently a missing gap of "multi-body non-rigid SFM", in which the task would be to jointly reconstruct and segment multiple 3D structures of the multiple, non-rigid objects or deformable scenes from images. Such a multi-body non-rigid scenario is common in reality (e.g. two persons shaking hands, multi-person social event), and how to solve it represents a natural {next-step} in SFM research. By leveraging recent results of subspace clustering, this paper proposes, for the first time, an effective framework for multi-body NRSFM, which simultaneously reconstructs and segments each 3D trajectory into their respective low-dimensional subspace. Under our formulation, 3D trajectories for each non-rigid structure can be well approximated with a sparse affine combination of other 3D trajectories from the same structure (self-expressiveness). We solve the resultant optimization with the alternating direction method of multipliers (ADMM). We demonstrate the efficacy of the proposed framework through extensive experiments on both synthetic and real data sequences. Our method clearly outperforms other alternative methods, such as first clustering the 2D feature tracks to groups and then doing non-rigid reconstruction in each group or first conducting 3D reconstruction by using single subspace assumption and then clustering the 3D trajectories into groups.Comment: 21 pages, 16 figure

A closed-form solution to estimate uncertainty in non-rigid structure from motion

Semi-Definite Programming (SDP) with low-rank prior has been widely applied in Non-Rigid Structure from Motion (NRSfM). Based on a low-rank constraint, it avoids the inherent ambiguity of basis number selection in conventional base-shape or base-trajectory methods. Despite the efficiency in deformable shape reconstruction, it remains unclear how to assess the uncertainty of the recovered shape from the SDP process. In this paper, we present a statistical inference on the element-wise uncertainty quantification of the estimated deforming 3D shape points in the case of the exact low-rank SDP problem. A closed-form uncertainty quantification method is proposed and tested. Moreover, we extend the exact low-rank uncertainty quantification to the approximate low-rank scenario with a numerical optimal rank selection method, which enables solving practical application in SDP based NRSfM scenario. The proposed method provides an independent module to the SDP method and only requires the statistic information of the input 2D tracked points. Extensive experiments prove that the output 3D points have identical normal distribution to the 2D trackings, the proposed method and quantify the uncertainty accurately, and supports that it has desirable effects on routinely SDP low-rank based NRSfM solver.Comment: 9 pages, 2 figure

Shape Interaction Matrix Revisited and Robustified: Efficient Subspace Clustering with Corrupted and Incomplete Data

The Shape Interaction Matrix (SIM) is one of the earliest approaches to performing subspace clustering (i.e., separating points drawn from a union of subspaces). In this paper, we revisit the SIM and reveal its connections to several recent subspace clustering methods. Our analysis lets us derive a simple, yet effective algorithm to robustify the SIM and make it applicable to realistic scenarios where the data is corrupted by noise. We justify our method by intuitive examples and the matrix perturbation theory. We then show how this approach can be extended to handle missing data, thus yielding an efficient and general subspace clustering algorithm. We demonstrate the benefits of our approach over state-of-the-art subspace clustering methods on several challenging motion segmentation and face clustering problems, where the data includes corrupted and missing measurements.Comment: This is an extended version of our iccv15 pape

Deformable motion 3D reconstruction by union of regularized subspaces

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper presents an approach to jointly retrieve camera pose, time-varying 3D shape, and automatic clustering based on motion primitives, from incomplete 2D trajectories in a monocular video. We introduce the concept of order-varying temporal regularization in order to exploit video data, that can be indistinctly applied to the 3D shape evolution as well as to the similarities between images. This results in a union of regularized subspaces which effectively encodes the 3D shape deformation. All parameters are learned via augmented Lagrange multipliers, in a unified and unsupervised manner that does not assume any training data at all. Experimental validation is reported on human motion from sparse to dense shapes, providing more robust and accurate solutions than state-of-the-art approaches in terms of 3D reconstruction, while also obtaining motion grouping results.Peer ReviewedPostprint (author's final draft

Unsupervised 3D reconstruction and grouping of rigid and non-rigid categories

© 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper we present an approach to jointly recover camera pose, 3D shape, and object and deformation type grouping, from incomplete 2D annotations in a multi-instance collection of RGB images. Our approach is able to handle indistinctly both rigid and non-rigid categories. This advances existing work, which only addresses the problem for one single object or, they assume the groups to be known a priori when multiple instances are handled. In order to address this broader version of the problem, we encode object deformation by means of multiple unions of subspaces, that is able to span from small rigid motion to complex deformations. The model parameters are learned via Augmented Lagrange Multipliers, in a completely unsupervised manner that does not require any training data at all. Extensive experimental evaluation is provided in a wide variety of synthetic and real scenarios, including rigid and non-rigid categories with small and large deformations. We obtain state-of-the-art solutions in terms of 3D reconstruction accuracy, while also providing grouping results that allow splitting the input images into object instances and their associated type of deformation.Peer ReviewedPostprint (author's final draft

Piecewise Bézier space: recovering 3D dynamic motion from video

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper we address the problem of jointly retrieving a 3D dynamic shape, camera motion, and deformation grouping from partial 2D point trajectories in a monocular video. To this end, we introduce a union of piecewise Bézier subspaces with enforcing continuities to model 3D motion. We show that formulating the problem in terms of piecewise curves, allows for a better physical interpretation of the resulting priors and a more accurate representation of the motion. An energy-based formulation is presented to solve the problem in an unsupervised, unified, accurate and efficient manner, by means of the use of augmented Lagrange multipliers. We thoroughly validate the approach on a wide variety of human video sequences, including those cases with noisy and missing observations, and providing more accurate joint estimations than state-of-the-art approaches.This work has been partially supported by the Spanish Ministry of Science and Innovation under project HuMoUR TIN2017-90086-R, by the ERA-Net Chistera project IPALM PCI2019-103386, and the María de Maeztu Seal of Excellence to IRI MDM-2016-0656Peer ReviewedPostprint (author's final draft

DUST: dual union of spatio-temporal subspaces for monocular multiple object 3D reconstruction

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.We present an approach to reconstruct the 3D shape of multiple deforming objects from incomplete 2D trajectories acquired by a single camera. Additionally, we simultaneously provide spatial segmentation (i.e., we identify each of the objects in every frame) and temporal clustering (i.e., we split the sequence into primitive actions). This advances existing work, which only tackled the problem for one single object and non-occluded tracks. In order to handle several objects at a time from partial observations, we model point trajectories as a union of spatial and temporal subspaces, and optimize the parameters of both modalities, the non-observed point tracks and the 3D shape via augmented Lagrange multipliers. The algorithm is fully unsupervised and results in a formulation which does not need initialization. We thoroughly validate the method on challenging scenarios with several human subjects performing different activities which involve complex motions and close interaction. We show our approach achieves state-of-the-art 3D reconstruction results, while it also provides spatial and temporal segmentation.Peer ReviewedPostprint (author's final draft